On beyond hidden source estimates—Improving the output of blind source separation algorithms

Abstract

In the presence of multiple simultaneously active acoustic sources, microphone response signals are typically additive mixtures of “acoustic images”—that is, filtered and delayed versions of hypothetical yet intangible “source signals.” Under certain conditions, Blind Source Separation (BSS) algorithms can “demix” sets of such microphone responses into output signals often called “Hidden Source Estimates” and characterized as estimates of those inaccessible source signals. However, despite the name of these algorithms and the characterization of their outputs, BSS algorithms generally do not actually reconstruct the original source signals. Indeed, it is not even clear that the notion of “source signal” is always well-defined. We argue that a valid BSS output can best be understood as an estimate of some unknown member of an entire equivalence class of related signals, and that certain members of these classes are much more useful and ontologically well-grounded than others. Notably, acoustic images are particularly interesting members of these equivalence classes. We present a method for converting arbitrary hidden source estimates into acoustic images, and explore the utility of enhancing BSS algorithms so that they output specific acoustic images rather than generic hidden source estimates.